[ChrisV]

His preflop limp was an attempt to lure you into a desperation push. Nines are a very strong hand heads up and you're nuts if you think this was him speculating with a low-mid pair. There's no way he would have limped here with 33, for example. FWIW, there are a lot of players I would try the desperation push against here (ComeOnPhish is not one of them).

After the flop, with the pot over two thirds of your stack, your push could be literally anything. Kx is impossible for you, or should be, since you would have pushed preflop, and on the flop would check to induce a steal. Good jacks and tens (JT and up) are likewise impossible. The only hands he's worried about you holding are bad jacks and tens, assuming you don't check to induce a steal with those hands too (I would). But even against those hands he wins 25% of the time thanks to his 6 outs and backdoor straight possibilities. I think it's an OK call, bit questionable. I'm not sure if I would have made it. I'd have to think there's some chance of you having pushed with a hopeless hand.